coxdev

A high-performance C++ for computing Cox proportional hazards model deviance, gradients, and Hessian information matrices. Built with Eigen for ease of use in R and Python, this library provides efficient survival analysis computations with support for different tie-breaking methods.

Features

• High Performance: C++ implementation with Eigen linear algebra library
• Comprehensive Support: Handles both Efron and Breslow tie-breaking methods
• Left-Truncated Data: Support for left-truncated survival data
• Efficient Computations: Optimized algorithms for deviance, gradient, and Hessian calculations
• Memory Efficient: Uses linear operators for large-scale computations
• Cross-Platform: Works on Linux, macOS, and Windows

Installation

Prerequisites

This package requires the Eigen C++ library headers. The Eigen library is included as a git submodule.

1. Initialize Eigen submodule: The Eigen library is included as a git submodule. Make sure it's initialized:

   git submodule update --init --recursive
   

Standard Installation

pip install .

With Custom Eigen Path

If you have Eigen installed elsewhere, you can specify its location:

env EIGEN_LIBRARY_PATH=/path/to/eigen pip install .

Development Installation

pip install .[dev]
pip install -e . --no-build-isolation

Quick Start

import numpy as np
from coxdev import CoxDeviance

# Generate sample survival data
n_samples = 1000
event_times = np.random.exponential(1.0, n_samples)
status = np.random.binomial(1, 0.7, n_samples)  # 70% events, 30% censored
linear_predictor = np.random.normal(0, 1, n_samples)

# Create CoxDeviance object
coxdev = CoxDeviance(event=event_times, status=status, tie_breaking='efron')

# Compute deviance and related quantities
result = coxdev(linear_predictor)

print(f"Deviance: {result.deviance:.4f}")
print(f"Saturated log-likelihood: {result.loglik_sat:.4f}")
print(f"Gradient norm: {np.linalg.norm(result.gradient):.4f}")

Advanced Usage

Left-Truncated Data

# With start times (left-truncated data)
start_times = np.random.exponential(0.5, n_samples)
coxdev = CoxDeviance(
    event=event_times, 
    status=status, 
    start=start_times,
    tie_breaking='efron'
)

Computing Information Matrix

# Get information matrix as a linear operator
info_matrix = coxdev.information(linear_predictor)

# Matrix-vector multiplication
v = np.random.normal(0, 1, n_samples)
result_vector = info_matrix @ v

# For small problems, you can compute the full matrix
X = np.random.normal(0, 1, (n_samples, 10))
beta = np.random.normal(0, 1, 10)
eta = X @ beta

# Information matrix for coefficients: X^T @ I @ X
I = info_matrix @ X
information_matrix = X.T @ I

Different Tie-Breaking Methods

# Efron's method (default)
coxdev_efron = CoxDeviance(event=event_times, status=status, tie_breaking='efron')

# Breslow's method
coxdev_breslow = CoxDeviance(event=event_times, status=status, tie_breaking='breslow')

API Reference

CoxDeviance

The main class for computing Cox model quantities.

Parameters

• event: Event times (failure times) for each observation
• status: Event indicators (1 for event occurred, 0 for censored)
• start: Start times for left-truncated data (optional)
• tie_breaking: Method for handling tied event times ('efron' or 'breslow')

Methods

• __call__(linear_predictor, sample_weight=None): Compute deviance and related quantities
• information(linear_predictor, sample_weight=None): Get information matrix as linear operator

CoxDevianceResult

Result object containing computation results.

Attributes

• linear_predictor: The linear predictor values used
• sample_weight: Sample weights used
• loglik_sat: Saturated log-likelihood value
• deviance: Computed deviance value
• gradient: Gradient of deviance with respect to linear predictor
• diag_hessian: Diagonal of Hessian matrix

Performance

The library is optimized for performance:

• C++ Implementation: Core computations in C++ with Eigen
• Memory Efficient: Reuses buffers and uses linear operators
• Vectorized Operations: Leverages Eigen's optimized linear algebra
• Minimal Python Overhead: Heavy computations done in C++

Building from Source

Prerequisites

• C++ compiler with C++17 support
• Eigen library headers
• For Python library: Python >= 3.9 + pybind11

Testing

Run the test suite:

pip install .[test]
python -m pytest tests/

Contributing

1. Fork the repository
2. Create a feature branch
3. Make your changes
4. Add tests for new functionality
5. Ensure all tests pass
6. Submit a pull request

License

This project is licensed under the BSD-3-Clause License - see the LICENSE file for details.

Citation

If you use this library in your research, please cite:

@software{coxdev2024,
  title={coxdev: High-performance Cox proportional hazards deviance computation},
  author={Taylor, Jonathan and Hastie, Trevor and Narasimhan, Balasubramanian},
  year={2024},
  url={https://github.com/jonathan-taylor/coxdev}
}

Acknowledgments

• Built with Eigen for efficient linear algebra
• Uses pybind11 for Python bindings
• Inspired by the R glmnet package for survival analysis